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21.
22.
Lamellar crystals of diblock, triblock and four-arm poly(ethylene glycol)-b-poly(ε-caprolactone) (PEG-b-PCL) crystalline-crystalline copolymers were successfully obtained from their solution. Morphology and structure of lamellar crystals of crystalline-crystalline copotymers were investigated using tapping-mode atomic force microscopy (AFM) and selected area electron diffraction (SAED). All of these samples showed the truncated-lozenge multilayer basal shapes with central screw dislocation or central stack, which were all obtained simultaneously from the oil bath. The diffraction pattern of PEG block lamellar crystal is attributed to the (120) diffracting planes and the pattern of PCL block lamellar crystal is attributed to the (1 I0) diffracting planes and (200) diffracting planes according to the SAED results. Four (110) crystal growth planes and two (200) crystal growth planes are discovered for the PCL blocks, but the (120) crystal growth planes of PEG blocks are hided in the figure of AFM. The crystalline structure of the four-arm copolymers (FA) is more disorder and confused than that of the diblock (DI) copolymer and the striated fold surface structures of lamellar crystals of four-arm copolymers (FA) are smoother than these of linear analogues, owing to the confused crystallization of blocks caused by the mutual restriction of blocks and the hindrance of the dendritic cores. In addition, the aspect ratio of FA is greater than that of the others. It is hypothesized that there are two reasons for the change of aspect ratios. First, the (200) diffracting planes of PCL crystals grew slowly compared to their (110) diffracting planes because of difference in the energy barrier. Secondly, edge dislocations on the (200) diffracting planes are also responsible for the variation of the aspect ratio. Consequently, the crystalline defects are augmented by the competing blocks crystallized simultaneously and the hindrance of the dendritic cores. 相似文献
23.
An exact method based on Green's equation is used to find the diffusion-controlled faradaic current for certain electrode geometries that incorporate edges and vertices. Thereby the magnitudes of the time-independent current density associated with angled electrode/electrode and electrode/insulator junctions are calculated. As well, the square-root-of-time-dependent currents associated with vertices, receive attention. These terms extend to longer times, the Cottrell formulation appropriate for short times. Though most of the problems solved here have been tackled previously, the novel Green function approach is shown to be straightforward and intuitive. 相似文献
24.
In this work, the electrochemical behavior of ferrocene (Fc) was investigated by cyclic voltammetry (CV) in room temperature ionic liquids (RTILs) of 1‐ethyl‐3‐methylimidazolium tetrafluoroborate (EMIBF4) on glass carbon (GC), edge plane pyrolytic graphite (EPPG) and multi‐walled carbon nanotube (MWCNTs)‐modified EPPG electrodes, respectively. The results demonstrated that on GC electrode, pairs of well‐defined reversible peaks were observed, while for the electrode of EPPG, the peak potential separation (ΔEp) is obviously larger than the theoretical value of 59 mV, hinting that the electrode of EPPG is distinguished from the commonly used electrode, consistent with the previous proposition that EPPG has many “defects”. To obtain an improved electrochemical response, multi‐walled carbon nanotubes (MWCNTs) were modified on the electrode of EPPG; the increased peak current and promoted peak potential separation not only proved the existence of “defects” in MWCNTs, but also supported that “creating active points” on an electrode is the main contribution of MWCNTs. Initiating the electrochemical research of Fc on the MWCNTs‐modified EPPG electrode in RTILs and verifying the presence of “defects” on both EPPG and MWCNTs using cyclic voltammograms (CVs) of Fc obtained in RTILs of EMIBF4, is the main contribution of this preliminary work. 相似文献
25.
Eric M. Rains 《The Ramanujan Journal》2009,18(3):257-306
In Ann. Math., to appear, 2008, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore
more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular,
we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely
formal limits) are indeed limiting cases. We also obtain a number of new trigonometric (q-hypergeometric) integral identities as limits from the elliptic level.
The author was supported in part by NSF Grant No. DMS-0401387. 相似文献
26.
Lech Zielinski 《Mathematical Physics, Analysis and Geometry》1999,2(3):291-321
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients. 相似文献
27.
本文从理论上讨论了低通滤波后二维图象中弯曲边缘的定位误差问题.边缘位置通常由二阶导数算子的零交叉点定义.研究表明:梯度方向上的二阶导数算子(secondderivativein gradient direction SDGD)产生向心的、可预测的边缘偏移;而线性拉普拉斯算子(Laplacian Operator)产生相反方向(离心)的可预测位置偏移.由此可推断:两者之和——称之为PLUS,将产生比其组成成份(SDGD 和 Laplace)更为精确的边缘定位算子.文章讨论了常用的低通滤波器(如 Gaussian 滤波器及 Tepee 滤波器)对边缘定位精度的影响. 相似文献
28.
Let X
1, X
2,... be a sequence of i.i.d. non-negative random variables with heavy tails. W e study logarithmic asymptotics for the distributions of the partial sums S
n
= X
1 + ··· + X
n
. Our main interest is in the crude estimates P(S
n
> n
x
) n
–x + 1 for appropriate values of x where is a specific parameter. The related conjecture proposed by Gantert (Stat. Probab. Lett. 49, 113–118) is investigated. 相似文献
29.
We consider a Dirichlettype problem for a system of elliptic equations of second order with a strong degeneracy at an inner point of the domain, when, in a neighborhood of this point, the principal term of the asymptotics of a solution is additionally given. We prove the existence and uniqueness of a solution of the problem considered in a weighted class of Hölder vector functions. 相似文献
30.